Elastic Stiffnesses 
Definition:  In the absence of thermal and electrical effects, the elastic stiffnesses C_{pq} of an anisotropic material are defined by the generalized Hooke's law, a 4th order tensor equation: σ = C ε or ε = S σ, respectively, with σ = stress tensor, C = tensor of the elastic stiffnesses, S = tensor of the elastic compliances, and ε = strain tensor. Because of the symmetry of σ and ε the number of independent components of C and S is reduced from 81 to 36. Hence, the elastic stiffnesses and C_{pq} and elastic compliances S_{pq} may be written as a 6x6 array and the strain and stress tensors as 6component vectors. Due to energy reasons this 6x6 array is symmetrical as well and the number of independent components C_{pq} is reduced to a maximum of 21. The existence of symmetry elements in the material leads to a further reduction of independent C and S components; in the case of isotropic media to 2 components. Essential properties of the deformation can then be described by the modulus of elasticity E and the Poisson's ratio ν. For onedimensional deformations Hooke's equation is reduced to σ = E ε. 
Units:  Pa 
Symbol:  c_{pq} (p = 1...6, q=1...6) C_{pq} (p = 1...6, q=1...6) 
Translation: 
DEElastizitätsmoduln
FRModules d'élasticité 
Sources

 Title  Author(s)  Medium  Location  Rank  Quality  Rating  Quantity  Source type  Systems 
 LandoltBörnstein: New Series = Neue Serie Gruppe 3 Vol. 1: Elastic, Piezoelectric, Piezooptic, and Electrooptic Constants of Crystals   Print  8 F  1  1 
  Data (measured)  Inorganic Compounds
Elements
Metals
Alloys
Minerals 
 LandoltBörnstein: New Series = Neue Serie Gruppe 3 Vol. 2: Crystal and Solid State Physics = Kristall und Festkörperphysik Elastic, Piezoelectric, Piezooptic, Electrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals   Print  8 F  1  1 
  Data (measured)  Inorganic Compounds
Elements
Metals
Alloys
Minerals 
 LandoltBörnstein: New Series = Neue Serie Gruppe 3 Vol. 11: Elastic, Piezoelectric, Pyroelectric, Piezooptic, Elektrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals   Print  8 F  1  1 
  Data (measured)  Inorganic Compounds
Elements
Metals
Alloys
Minerals 
 LandoltBörnstein: New Series = Neue Serie Gruppe 3 Vol. 18: Elastic, Piezoelectric, Pyroelectric, Piezooptic, Elektrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals   Print  8 G  1  1 
  Data (measured)  Inorganic Compounds
Elements
Metals
Alloys
Minerals 
 Single Crystal Elastic Constants and Calculated Aggregate Properties : a Handbook  Simmons Gene ; Wang Herbert  Print  NEBIS  1  2 
  Data (measured)  Inorganic Compounds
Elements
Metals
Alloys
Minerals
Benzene 
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